Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Boundary singularities of positive solutions of quasilinear Hamilton-Jacobi equations

Abstract : We study the boundary behaviour of the solutions of (E) $\;-\Gd_p u+|\nabla u|^q=0$ in a domain $\Gw \sbs \BBR^N$, when $N\geq p> q > p-1$. We show the existence of a critical exponent $q_* < p$ such that if $p-1 < q < q_*$ there exist positive solutions of (E) with an isolated singularity on $\prt\Gw$ and that these solutions belong to two different classes of singular solutions. If $q_*\leq q < p$ no such solution exists and actually any boundary isolated singularity of a positive solution of (E) is removable. We prove that all the singular positive solutions are classified according the two types of singular solutions that we have constructed.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01095162
Contributor : Laurent Veron <>
Submitted on : Saturday, February 28, 2015 - 5:45:54 PM
Last modification on : Tuesday, August 13, 2019 - 2:30:11 PM
Document(s) archivé(s) le : Friday, May 29, 2015 - 10:15:28 AM

Files

Bound18_mgh.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01095162, version 3
  • ARXIV : 1412.4613

Citation

Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Véron. Boundary singularities of positive solutions of quasilinear Hamilton-Jacobi equations. 2015. ⟨hal-01095162v3⟩

Share

Metrics

Record views

61

Files downloads

24